1. Field of the Invention
The present invention relates to power supplies and more precisely to the operation of power supplies for which the curve of the power supplied as a function of the voltage at the terminals of the supply features a maximum.
For a power supply of the above kind, the power supplied is at a maximum when the voltage has a given value. For optimum use of the power supply—to draw maximum power therefrom—it is advantageous for the voltage at the terminals of the supply to be as equal to the aforementioned given value as often as possible.
2. Description of the Prior Art
The solar generators used for satellites constitute one example of a power supply of the above kind. FIG. 1 shows a graph of the current and the power as a function of the voltage at the terminals of a generator, in the case of a generator formed by a series connection of a multiplicity of Si BSR (Back Surface Reflector) cells; cells of this kind are available in the aerospace industry. The current in amperes supplied by the solar generator and the power in watts delivered by the solar generator are plotted on the ordinate axis; the voltage in volts at the terminals of the solar generator is plotted on the abscissa axis. Curves 1 and 2 in FIG. 1 correspond to operation at a temperature of +100° C.; curves 3 and 4 correspond to operation at a temperature of −100° C. Curve 2 in FIG. 1 is a graph of current as a function of voltage and shows that the current supplied by the cells falls when the voltage exceeds a value of the order of 35 V, which is explained by a cell saturation phenomenon; the curve 4 is similar, except that the saturation voltage is of the order of 75 V. Curve 1 in FIG. 1 is a graph of the power supplied by the solar generator and shows that the power supplied features a maximum which in this example has a value of the order of 100 W and is achieved for a value V0 of the voltage that is of the order of 38 V. Curve 4 is similar to curve 2, with a maximum power of the order of 200 W and a voltage V0 of the order of 70 V. These curves constitute only one particular example of a generator in which the graph of the power supplied as a function of the output voltage features a maximum.
To use a solar generator of the above kind, or more generally a power supply of the above kind, it is advantageous for the voltage at the terminals of the supply to be as close as possible to the value V0 of the voltage at which the power supply delivers maximum power. This problem is particularly acute in the case of solar generators used in satellites, for which the voltage V0 at which the power supplied by the solar generator is at a maximum varies as a function of the temperature to which the solar generator is subjected, as shown in FIG. 1; the voltage V0 also varies as a function of:                the intensity of the solar radiation to which the generator is exposed, and        aging of the generator.        
For a satellite in low Earth orbit, the temperature can typically vary in a range from −100° C. to +100° C. The intensity of the solar radiation can vary as a function of the distance from the Sun; for a mission from the Earth to Mars, the intensity of the solar radiation can vary in a ratio of 3 to 1. Aging of the generator causes the short circuiting of some cells. Overall, the voltage V0 can typically vary in a ratio of 1 to 2, for example from 40 to 80V.
Thus one of the major difficulties to be overcome in predicting the optimum operating point lies in the dependence of the power delivered by a solar generator on parameters such as the incident solar energy, which is a function of the position of the cells relative to the light rays, the temperature of cells exposed to sunlight but dissipating energy by reflection and conduction toward the shaded rear surface, and, finally, aging of the cells and deterioration thereof caused by the environment, such as microcracks and meteorite impacts.
Another problem relates to the nature of the parameter to be optimized, i.e. the electrical power, which cannot be sensed directly. The two electrical parameters that can be measured directly are the current and the voltage of a cell or of the solar generator. The power is the result of multiplying the instantaneous values of these parameters. Determining the maximum power amounts to calculating the derivative of the instantaneous power as a function of the current or of the voltage and slaving the derivative to a null value. All maximum power point tracking (MPPT) algorithms that track this derivative employ excitation of the operating point of the solar generator with the aid of a DC/DC converter allowing excursion of this point around its optimum position without being able to fix thereto in a durable manner.
The design of an MPPT converter with efficiency and stability performance enabling long-term use in space has not led to this principle being competitive with concepts based on the distribution of a voltage regulated with the aid of sequential switching shunt regulators (S3R) or sequential switching shunt and series regulators (S4R) for geostationary Earth orbit (GEO) satellites.
The increasingly frequent use of low Earth orbit (LEO) satellites with arrangements, known as constellations, of several dozen satellites with powers of a few kW has returned MPPT concepts to the agenda. The essential reason is that, on such missions, involving frequent eclipses with short sunlit periods, of the order of 60 minutes, the load network employs units operating in high intensity power pulse mode. This type of use represents a severe constraint on the battery, which must be recharged rapidly at high currents over short periods. It is evident that, in this context, the solar generator has an essential role and that it is apparently necessary to bias it to its maximum power point, as otherwise it may have a rating that is higher than is strictly necessary.
The characteristics of the optimum operating point are explained hereinafter.
A solar generator is constituted of an assembly of identical solar cells in an array formed of m rows each containing n cells in series, and the electrical characteristic of a solar generator is an image of the electrical behavior of a cell.
A cell is defined by four electrical parameters, the short circuit current iSC, the open circuit voltage vOC and the current-voltage coordinates iMP and vMP of the optimum point known as the maximum power point (MPP). These parameters are specified under standard conditions of illumination and temperature T0 at the start of life. They are therefore liable to evolve as a function of the temperature T of the cell, whence:                                                         i              SC                        ⁡                          (              T              )                                =                                                    i                SC                            ⁡                              (                                  T                  0                                )                                      +                                          (                                  T                  -                                      T                    0                                                  )                            ⁢                                                ⅆ                                      i                    SA                                                                    ⅆ                  T                                                                    ⁢                                  ⁢                                            v              OC                        ⁡                          (              T              )                                =                                                    v                OC                            ⁡                              (                                  T                  0                                )                                      +                                          (                                  T                  -                                      T                    0                                                  )                            ⁢                                                ⅆ                                      v                    OC                                                                    ⅆ                  T                                                                    ⁢                                  ⁢                                            i              MP                        ⁡                          (              T              )                                =                                                    i                MP                            ⁡                              (                                  T                  0                                )                                      +                                          (                                  T                  -                                      T                    0                                                  )                            ⁢                                                ⅆ                                      i                    MP                                                                    ⅆ                  T                                                                    ⁢                                  ⁢                                            v              MP                        ⁡                          (              T              )                                =                                                    v                MP                            ⁡                              (                                  T                  0                                )                                      +                                          (                                  T                  -                                      T                    0                                                  )                            ⁢                                                ⅆ                                      v                    MP                                                                    ⅆ                  T                                                                                        (        2.1        )            
The cell is also described by its mechanical parameters, namely its length L, width I, and thickness e. The power PS received by the cell is proportional to its surface area S, i.e.:                               P          S                =                              P            0                    Ll                                    (        2.20`        )            
in which P0 is the power per m2 supplied by the Sun, that is to say 1 230 W/m2, or the light source. The cell transforms this light power into electrical power PMP with an efficiency η such that:                     η        =                                                                              v                  MP                                ⁡                                  (                  T                  )                                            ⁢                                                i                  MP                                ⁡                                  (                  T                  )                                                                    P              S                                =                                    P              MP                                      P              S                                                          (        2.3        )            
The electrical characteristics of a solar cell correspond to evolutions of the current iSA and the power PSA delivered thereby as a function of the voltage vSA at its terminals. Tada and Carter have studied modeling of the electrical behavior of the cell, which corresponds to the following equations:                                                         i              SA                        ⁡                          (              t              )                                =                                                    i                SC                            ⁡                              (                t                )                                      -                                          i                R                            ⁡                              (                                                      exp                    ⁡                                          (                                                                                                    qv                            SA                                                    ⁡                                                      (                            t                            )                                                                          AkT                                            )                                                        -                  1                                )                                                    ⁢                                  ⁢                                            P              SA                        ⁡                          (              t              )                                =                                                    v                SA                            ⁡                              (                t                )                                      ⁢                                          i                SA                            ⁡                              (                t                )                                                                        (        2.4        )            
in which iR is the saturation current of the semiconductor junction and A is a parameter which defines the influence of diffusion and recombination phenomena and varies from 0.5 to 2.5. The value of the coefficient kT/q at 28° C. is 0.02596125.
FIG. 2 shows the evolutions of iSA(vSA) and PSA(vSA) at a time t at which the illumination and temperature conditions are defined for a cell characterized by its parameters as measured under standardized conditions.
The iSA(vSA) characteristic 5 (FIG. 2) is a continuous function, corresponding to an exponential function, and whose derivative is always negative. On the other hand, the PSA(vSA) characteristic 6 (FIG. 2) has a maximum at the voltage vMPP which is the voltage of the maximum power point MPP. The associated current of the cell is iMPP. The same approach can be adopted by selecting the characteristics vSA(iSA) and PSA(iSA), which leads to identifying the coordinates of the optimum point from the following equations:                                                         ⅆ              P                                      ⅆ                              v                SA                                              =                                                    ⅆ                P                                            ⅆ                                  i                  SA                                                      =            0                          ⁢                                  ⁢        or                            (        2.5        )                                                      ⅆ                          v              SA                                            ⅆ                          i              SA                                      =        1                            (        2.6        )            
The properties of the maximum power point are therefore characterized by the fact that the derivatives of the operating points situated to the left of the MPP are positive whereas those of points situated to its right are negative.
This property can be exploited in dynamic operation by observing that any variation dvSA about a point M to the right of the MPP leads to a variation diSA of the same sign. A change of phase is introduced if the point M is to the left of the MPP.
Finally, the absolute value of the tangent to the characteristic iSA(vSA) at the MPP is 45° (π/4). For points to its left its value is from 0 to π/4. For points to the right of the MPP, it is from π/4 to π/2.
The basic principles of maximum power point tracking (MPPT) are described next.
The characteristic ISA(VSA) of a solar generator with m rows, also known as strings, each constituted of n cells in series, is of the following form, where RS is the series resistance of the cell:                               I          SA                =                  m          ⁡                      (                                          i                SC                            -                                                i                  R                                ⁡                                  (                                                            exp                      ⁡                                              (                                                                              q                            nAkT                                                    ⁢                                                      (                                                                                          V                                SA                                                            +                                                                                                n                                  m                                                                ⁢                                                                  R                                  S                                                                ⁢                                                                  I                                  SA                                                                                                                      )                                                                          )                                                              -                    1                                    )                                                      )                                              (        2.7        )            
It is often useful to use the inverse function, which results in using the VSA(ISA) characteristic, expressed as follows:                               V          SA                =                                            nAkT              q                        ⁢                          Log              ⁡                              (                                  1                  +                                                                                    i                        SC                                            -                                                                        I                          SA                                                m                                                                                    i                      R                                                                      )                                              -                                    n              m                        ⁢                          R              S                        ⁢                          I              SA                                                          (        2.8        )            
The instantaneous power PSA(t) of the solar generator is the product of the instantaneous voltage VSA(t) and the instantaneous current ISA(t), both measured at time t:PSA(t)=VSA(t)ISA(t)  (2.9)
Biasing the solar generator to its MPP implies a knowledge of the coordinates of that point. This point can be determined only by exploiting the properties of the MPP. If the concepts based on the use of conventional DC/DC converters whose control is based on computing the tangent to the ISA(VSA) characteristic and locking it to the value π/4 are eliminated, the general principle of MPP tracking is based on differentiating equation 2.9, yielding:dPSA(t)=ISA(t)dVSA(t)+VSA(t) dISA(t)  (2.10)
Determining the optimum operating point amounts to finding the maximum of the function PSA(t), i.e. solving the equation:0=ISA(t)dVSA(t)+VSA(t)dISA(t)  (2.11)
i.e.:                                           ⅆ                                          V                SA                            ⁡                              (                t                )                                                          ⅆ                                          I                SA                            ⁡                              (                t                )                                                    =                  -                                                    V                SA                            ⁡                              (                t                )                                                                    I                SA                            ⁡                              (                t                )                                                                        (        2.12        )            
Interpreting this equation indicates that the MPP corresponds to the intersection of the straight load line and the differential impedance of the generator.
Although determining ISA and VSA is not problematical, the same cannot be said of the differential impedance. One way to measure it consists in using a time differential such that:                                           ⅆ                          V              SA                                            ⅆ                          I              SA                                      =                                            ⅆ                              V                SA                                                    ⅆ              t                                                          ⅆ                              I                SA                                                    ⅆ              t                                                          (        2.13        )            
Computing this impedance amounts to differentiating the values of ISA and VSA already measured to evaluate the straight load line. The technical difficulty lies in managing the division of these magnitudes. As a general rule, solving equation (2.13) requires a dynamic maximum power point tracking (MPPT) algorithm. Prior art MPPT systems differ in the type of algorithm employed. Those most widely used and their associated drawbacks are cited below.
In the control systems currently used, maximum power point tracking is based on permanent tracking of the maximum power point excitation of the solar generator with the objective of tracking with as small a difference as possible:                A first method detects crossing of the MPP. This method is that most widely used. It consists in traveling along the PS(VSA) characteristic and detecting the time at which the MPP is crossed, in order to return to it and bracket it. Two methods can be employed.        
Crossing the MPP can be detected by detecting the peak power. This simple principle relies on a sampling process. The power PS(t) demanded of the generator is progressively perturbed, and then stored at regular time intervals TS. The comparison of the powers PS(t1) and PS(t2) between two successive samples taken at times t1 and t2 yields:                                                                         P                S                            ⁡                              (                                  t                  2                                )                                      -                                          P                S                            ⁡                              (                                  t                  1                                )                                                                        t              2                        -                          t              1                                      =                              ⅆ                          P              S                                            ⅆ            t                                              (        2.14        )            
If dPS/dt is positive, the operating point is to the left of the MPP, the sign of the perturbation is not modified, and the perturbation must evolve toward increasing powers demanded of the solar generator. The detection of a negative dPS/dt indicates that the MPP has been crossed and that the sign of the perturbation must be reversed. The power PS(t) is generally stored in memory by a zero order blocker or peak detector. The perturbation is generally obtained by means of a sawtooth operating on a current-controlled DC/DC converter.
Crossing the MPP can also be detected by detecting a change of phase. In this case, the perturbation is a sinusoidal signal of frequency ω applied to a DC/DC converter and which modulates the operating point of the solar generator by introducing therein a sinusoidal variation of low amplitude. The measured current ISA(t) reflects this perturbation with a possible phase-shift φ, with the result that:ISA(t)=ISA(0)+i sin(ωt+φ)  (2.15)
The measured voltage VSA(t) also reflects the sinusoidal modulation. The position of the operating point relative to the MPP is determined by comparing the phases. The phases are the same to the right of the MPP and opposite to its left.                A second method consists of detecting crossing the MPP by a logical process. The use of this approach will expand in the future, thanks to advances in microprocessors. The method consists in establishing a logical table in which the measured magnitude signs are taken into account to orient the MPPT direction. Observation of the characteristics ISA(VSA) and PS(VSA) indicates that, if the operating point is to the left of the MPP, then for any perturbation of duration dt:                               sign          ⁢                                    ⅆ                              P                S                                                    ⅆ              t                                      =                  sign          ⁢                                    ⅆ                              V                SA                                                    ⅆ              t                                                          (        2.16        )                    
The operating point is to the right of the MPP if, to the contrary:                               sign          ⁢                                    ⅆ                              P                S                                                    ⅆ              t                                      =                              -            sign                    ⁢                                    ⅆ                              V                SA                                                    ⅆ              t                                                          (        2.17        )            
It follows that a signal s(t) for orienting the direction of an excursion can be generated by activating a DC/DC converter according to the sign of:                                                         ⅆ                              P                S                                                    ⅆ              t                                ⁢                                    ⅆ                              V                SA                                                    ⅆ              t                                      =                  s          ⁡                      (            t            )                                              (        2.18        )            
If s(t)>0 the operating point M is such that VM<VMPP, and the DC/DC converter is deactivated to allow the potential of the solar generator to increase. If s(t)<0, the operating point of the solar generator has crossed the MPP and the DC/DC converter can be activated again. This approach does not necessitate sampling.
The above MPPT solving methods have serious drawbacks.                The most serious drawback of these methods is the necessity to insert between the solar generator and the load network units allowing independent evolutions of their potentials. To allow the solar generator to operate at its MPP, it is obligatory to assign it total freedom in terms of the evolution of its operating point. This is all the more important in that this point is excited continuously by an MPPT algorithm. The measurements effected bracket the MPP and vary the voltage of the solar generator around the MPP. Similarly, the voltage of the network is subject to different constraints, imposing either a regulated voltage V0 different from that of the MPP, or a battery voltage VB, which must be able to evolve freely according to whether the battery is charging or discharging. A consequence of the obligatory insertion of regulators between the GS and the network is the mass contribution and the energy take-off of these buffer units. All the maximum power of the solar generator has to pass through these units. The mass penalty is of the order of 3 g/W, which raises to 30 kg the mass of a unit of this kind for a satellite requiring 10 kW of power. From the efficiency point of view, these units continuously sample from approximately 7% to 10% of the power in transit. This has two consequences: firstly, an increase of approximately 10% in the performance of the GS in terms of mass, volume and power, and evacuation of the power dissipated by the regulators, which is of the order of 1 kW for an 11 kW GS, which leads to the use of heat pipes with the associated mass and energy constraints.        The major drawback of continuous tracking processes is the very necessity for continuous tracking, as their name indicates. Detection of the MPP necessarily entails a dynamic process that causes displacement of the operating point of the solar generator to measure the displacement and orient it toward the MPP. The MPP is detected only when it is crossed. The DC/DC converter cannot be slaved to the MPP, constantly oscillating about this point, which becomes an ideal equilibrium position that is never attained.        Furthermore, whatever tracking algorithm is used, detection of the MPP implies instantaneous measurements of ISA(t) and VSA(t) and, most importantly, the generation of the product ISA(t)VSA(t) to show up PS(t) or of ratios such as VSA(t)/ISA(t) or dVSA(t)/dISA(t) to determine differential and load impedances.        
These non-linear functions must be implemented in the analog domain as they are operative in the DC/DC converter regulation loop. The integrated circuits that carry out these operations have an accuracy that varies with their operating range and demand signals of matched amplitude.
Biasing a solar generator around its MPP requires a system whose functional organization is as shown in FIG. 3. It is characterized by a solar generator 7 whose instantaneous parameters VSA(t) and ISA(t) are picked up and transmitted to an MPPT management unit 8. The solar generator is connected to a Buck power cell which is responsible for transferring the power PS(t) to a load network RC at a regulated voltage V0. The role of the power cell is to isolate the generator from the network and to enable it to evolve optimally with excellent energy efficiency. The network voltage is slaved to the value V0 by a main error amplifier (MEA) control loop, which compares the voltage V0 to a reference voltage VREF. The switch Q of the power cell is controlled in pulse width modulation (PWM) mode by a driver module 10 in turn controlled by a priority management unit 11 which interfaces the MPPT and MEA control loops.
This priority management function biases the solar generator (GS) about the MPP if the power demand of the network requires it, by slaving the voltage VSA to the value VMPP+/−dV, i.e. by obligatory slaving of the power cell input voltage. The output voltage is no longer slaved to V0 and can therefore depart from that value. Control priority is assigned to the MPPT loop.
As soon as the power demand of the network decreases and no longer requires biasing of the GS to the MPPT, the MPPT loop is deactivated and the MEA loop returns to service. The output voltage of the power cell is again regulated.
The MPPT function is therefore a control loop integrated into the functioning of a power cell and takes priority over the conventional MEA control function of that unit. A priority selector function is therefore necessary to define the priority loop. The problem with this prior art is therefore that of control interference.
An objective of the present invention is therefore to remedy the drawbacks cited hereinabove.